Wave field synthesis is a sound wave field reproduction technique that overcomes the limitations of conventional surround sound methods. The essence of wave field synthesis is the synthesis of the physical properties of an acoustic wave field through a set of speakers within an extended listening region. The extended listening region is the main advantage of sound field reproduction with respect to other consumer standards such as stereophony or 5.1 systems.
The Kirchhoff-Helmholtz theorem is the main principle behind wave field synthesis. Based on this theorem, at any listening point within a source-free extended listening region, any arbitrary acoustic wave field can be uniquely determined if both the sound pressure and its directional gradient on the surface enclosing this listening region are known. More specifically according to this theorem, any arbitrary acoustic wave field can be synthesized by generating the sound pressure distribution of the target wave field and its directional gradient by monopole and dipole speakers, respectively, that have been distributed on the surface of the listening region.
According to the Kirchhoff-Helmholtz theorem, the precise synthesis of an acoustic wave field requires an infinite number of monopole and dipole speakers that have been distributed on the surface of the listening region. Of course, in reality the number of speakers must be finite, resulting in an approximation that introduces inaccuracies into the synthesized sound wave field as compared to the target wave field that corresponds to the virtual point source(s). More specifically, such approximation implies a spatial sampling process that results in spatial aliasing artifacts. Spatial sampling limits the exact reproduction of the target sound wave field to a given upper frequency referred to as the Nyquist frequency. Another practical problem is the assumption that speakers are ideal monopole and dipole speakers. However, in reality this assumption does not generally hold.